Poisson and near-symplectic structures on generalized wrinkled fibrations in dimension 6

Abstract

We show that generalized broken fibrations in arbitrary dimensions admit rank-2 Poisson structures compatible with the fibration structure. After extending the notion of wrinkled fibration to dimension 6 we prove that these wrinkled fibrations also admit compatible rank-2 Poisson structures. In the cases with indefinite singularities we can provide these wrinkled fibrations in dimension 6 with near-symplectic structures.

arXiv comment35 pages

References in corpus (8)

• 6D SCFTs and Phases of 5D Theories
• Singular Lefschetz pencils
• Wrinkled fibrations on near-symplectic manifolds
• Poisson brackets with prescribed Casimirs
• Poisson structures on smooth 4-manifolds
• Poisson structures on wrinkled fibrations
• Near-symplectic 2n-manifolds
• $G$-Invariant Deformations of Almost-Coupling Poisson Structures